The Republican-controlled House of Representatives delivered a rare rebuke to Barack Obama over his involvement in the Libyan war on Friday by rejecting a resolution to authorise the US mission.

It is an embarrassment for the president to have a vote go against him in time of conflict and reflects the disenchantment in the US over yet another war. The vote is primarily symbolic but members of Congress sympathetic to Obama and the US role in Libya said the danger was that it could leave the Libyan leader, Muammar Gaddafi, with the impression that support for the war is collapsing.

The House voted 295 to 123 against the resolution to authorise the war. About 70 of the president's Democratic party joined the Republicans to vote it down.

The vote was held to highlight a constitutional debate between the White House and Congress over presidents engaging in wars without congressional approval. It is the first time since during the Bosnian conflict in 1999 that either the House or the Senate has voted against a military operation. The Democratic-controlled Senate is unlikely to mirror the House vote.

The House ignored pleas by the secretary of state, Hillary Clinton, on Thursday against voting it down. Obama argues that he does not need congressional authorisation because the Libya mission is not a full-blown conflict.

House speaker John Boehner said: "I support the removal of the Libyan regime. I support the president's authority as commander-in-chief, but when the president chooses to challenge the powers of the Congress, I, as speaker of the House, will defend the constitutional authority of the legislature."

Republican congressman Tom Rooney, who sits on the armed services committee, said: "The last thing that we want as Americans is for some president, whether it's this president or some future president, to be able to pick fights around the world without any debate from another branch of government."

Rooney had sponsored a separate bill aiming to cut off funds to the Libya campaign, which would have barred drone attacks and air strikes but allowed the US to continue actions in intelligence gathering, refuelling and reconnaissance. The effort to cut off money was defeated by 238 votes to 180.

Republican leaders had backed the measure, but did not pressure other Republicans in the House to support it.

In a separate development, the Guardian has learned that Nato forces are confident they are successfully tracking Gaddafi as he moves from hideout to hideout in Tripoli.

The coalition is abiding by the UN mandate, which does not permit the military to target the Libyan leader directly, and commanders are hoping he will be removed by a revolt from within his circle of closest associates.

There is also a privately held wish in London that Gaddafi might be caught up in a legitimate bombing raid on a command and control cell as he flits from one safe haven to another. A senior British source, who spoke on condition of anonymity, said Gaddafi's movements were being monitored closely, and that the military had been able to track him "racing from one place to another" over recent weeks.

Nato has an array of surveillance equipment at its disposal: as well as a Nimrod plane and drones, HMS Liverpool, which is stationed off the Libyan coast, has listening systems which should enable the military to keep watch on the Libyan leader and his entourage.